Practice the questions given in the worksheet on application of Factor Theorem.

**1.** Find the roots of the equation 6z\(^{2}\) + 11z -10 = 0. Hence, factorize 6z\(^{2}\) + 11z -10.

**2.** Find the roots of the equation 2m\(^{2}\) - 3m - 6 = 0. Hence, factorize 2m\(^{2}\) - 3m - 6 = 0

**3.** Find the roots of the equation p(p + 1) - 4 = 0. Hence, factorize 4 - p - p\(^{2}\).

**4.** Find the quadratic equation whose roots are

(i) -3, 7

(ii) 2 + √3, 2 - √3

(iii) \(\frac{1}{√3}\), - \(\frac{1}{√3}\)

**5.** Find the cubic equation whose roots are

(i) 1, 2, 3

(ii) -4, √3, -√3

(iii) \(\frac{1}{2}\), \(\frac{√5}{2}\), \(\frac{-√5}{2}\)

Answers for the worksheet on application of Factor Theorem are given below:

**Answers:**

**1.** \(\frac{2}{3}\) , \(\frac{-5}{2}\); (3z - 2)(2z + 5)

**2.** \(\frac{3 + √57}{4}\), \(\frac{3 - √57}{4}\); (2m - \(\frac{3
+ √57}{2}\))(m - \(\frac{3 - √57}{4}\))

**3.** \(\frac{-1 + √17}{2}\), \(\frac{-1 - √17}{2}\); (\(\frac{-1
+ √17}{2}\) - p)( \(\frac{1 + √17}{2}\) + p)

**4.** (i) y\(^{2}\) - 4y -21 = 0

(ii) z\(^{2}\) - 4z + 1 = 0

(iii) 3p\(^{2}\) - 1 = 0

**5.** (i) z\(^{3}\) - 6z\(^{2}\) + 11z - 6

(ii) m\(^{3}\) + 4m\(^{2}\) - 3m - 12

(iii) 8k\(^{3}\) - 4k\(^{2}\) - 10k + 5 = 0

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